The Minister's Black Veil by Nathaniel Hawthorne

From Wikipedia:The story begins with the sexton standing in front of the meeting-house, ringing the bell. He is to stop ringing the bell when the Reverend Mr. Hooper comes into sight. However, the congregation is met with an unusual sight: Mr. Hooper is wearing a black semi-transparent veil that obscures all of his face but his mouth and chin from view.

By the next day, even the local children are talking of the strange change that seems to have come over their minister. Yet, no one is able to ask Mr. Hooper directly about the veil, except for his fiancée Elizabeth.